Known in the art is a diesel engine which arranges in an engine exhaust passage an NOx storage catalyst which stores NOx in exhaust gas when the air-fuel ratio of the inflowing exhaust gas is lean and releases the stored NOx when the air-fuel ratio of the inflowing exhaust gas is made rich, arranges downstream of the NOx storage catalyst in the engine exhaust passage an NOx selective reduction catalyst, makes the ammonia which is produced at the NOx storage catalyst when the exhaust gas which flows into the NOx storage catalyst is made rich be adsorbed at the NOx selective reduction catalyst, and reduce the NOx which is contained in the exhaust gas by the adsorbed ammonia (for example, see Patent Literature 1).
In this diesel engine, the amount of ammonia which is adsorbed at the NOx selective reduction catalyst is controlled to become the optimum amount for reduction of the NOx. However, the method of adsorption of ammonia includes a method of adsorption where the adsorbed ammonia is easily desorbed and a method of adsorption where the adsorbed ammonia is hard to desorb, that is, two methods of adsorption. When using the method of adsorption where the ammonia is easily desorbed, it is possible to easily reduce the NOx by the adsorbed ammonia, but when using the method of adsorption where the adsorbed ammonia is hard to desorb, it is impossible to easily reduce the NOx by the adsorbed ammonia. Therefore, when using the adsorbed ammonia to reduce the NOx, it is necessary to consider the method of adsorption of the ammonia.